Subgroups — #36537615

Order 22784.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031568	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031559	C₂	1	1	yes	maximal, characteristic
3	#26030575	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019799	C₂	1	2	yes	maximal, complemented
5	#26019785	C₂	1	2	yes	maximal, complemented
6	#26019703	C₂	1	2	yes	maximal, complemented
7	#26019689	C₂	1	2	yes	maximal, complemented
8	C₂×#19151351	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018943	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018930	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152155	C₂²	1	1	yes	characteristic
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151953	—	2	1	no	—
15	#19151953	—	2	1	no	—
16	#19151949	C₂²	1	1	yes	characteristic
17	#19151949	C₂²	1	1	yes	characteristic
18	#19151945	C₂²	1	1	yes	characteristic
19	#19151945	C₂²	1	1	yes	characteristic
20	#19151888	C₂²	1	2	yes	—
21	#19151880	—	2	1	no	—
22	#19151878	C₂²	1	2	yes	—
23	#19151875	—	2	1	no	—
24	#19151832	—	2	2	no	—
25	#19151825	—	2	2	no	—
26	#19151803	C₂²	1	2	yes	—
27	#19151795	—	2	1	no	—
28	#19151793	C₂²	1	2	yes	—
29	#19151790	—	2	1	no	—
30	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151595	—	2	1	no	—
33	#19151595	—	2	1	no	—
34	#19151351	C₂²	1	2	yes	—
35	#19151351	C₂²	1	2	yes	—
36	#19151346	C₂²	1	2	yes	—
37	#19151345	C₂²	1	2	yes	—
38	#19151343	C₂²	1	2	yes	—
39	#19151341	C₂²	1	2	yes	—
40	C₂×#131×C₈₉	—	2	1	no	—
41	#532×C₈₉	C₂²	1	1	yes	characteristic
42	#436×C₈₉	—	2	1	no	—
43	#436×C₈₉	C₂²	1	2	yes	—
44	C₈×D₄×C₈₉	—	2	1	no	—
45	C₈×D₄×C₈₉	C₂²	1	2	yes	—
46	#423×C₈₉	C₂²	1	1	yes	characteristic
47	#408×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	—	2	1	no	—
50	C₂×#13083562	—	2	2	no	—
51	C₂×#13083559	—	2	2	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂²×#10623494	—	2	1	no	—
54	#15668012	C₂³	1	1	yes	characteristic
55	#15668012	C₂³	1	1	yes	characteristic
56	#15668012	C₂³	1	1	yes	characteristic
57	#15668009	C₂³	1	1	yes	characteristic
58	#15668004	—	2	1	no	—
59	#15668000	—	2	1	no	—
60	#15667991	—	2	1	no	—
61	#15667991	—	2	1	no	—
62	#15667986	—	2	1	no	—
63	#15667986	—	2	1	no	—
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	—	2	1	no	—
66	C₄×D₃₅₆	—	2	1	no	—
67	C₄×D₃₅₆	—	2	1	no	—
68	#15667971	—	2	1	no	—
69	#15667945	—	2	2	no	—
70	#15667943	—	2	2	no	—
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	C₄⋊#10623494	C₂³	1	2	yes	—
75	#15667937	—	2	1	no	—
76	#15667937	—	2	1	no	—
77	#15667937	—	2	1	no	—
78	#15667937	—	2	1	no	—
79	#15667935	—	2	2	no	—
80	#15667934	—	2	1	no	—
81	#15667934	—	2	1	no	—
82	#15667934	—	2	1	no	—
83	#15667934	—	2	1	no	—
84	#15667933	—	2	2	no	—
85	#15667933	—	2	2	no	—
86	#15667932	—	2	2	no	—
87	C₂×#41×C₈₉	—	2	1	no	—
88	#131×C₈₉	—	4	4	no	—
89	C₂×M₁₆×C₈₉	—	2	1	no	—
90	C₂×M₁₆×C₈₉	—	2	2	no	—
91	C₂²×C₈×C₈₉	—	2	2	no	—
92	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
95	#127×C₈₉	D₄	1	1	yes	characteristic
96	#124×C₈₉	—	2	1	no	—
97	#121×C₈₉	—	2	1	no	—
98	#121×C₈₉	D₄	1	2	yes	—
99	C₄×D₄×C₈₉	—	2	1	no	—
100	C₄×D₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	—	2	1	no	—
103	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₈₉	—	2	2	no	—
105	C₂²⋊C₈×C₈₉	—	2	2	no	—
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	#13083574	—	4	2	no	—
111	#13083574	—	4	2	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×Dic₁₇₈	—	2	1	no	—
114	C₂×Dic₁₇₈	—	2	1	no	—
115	C₂×D₃₅₆	—	2	1	no	—
116	C₂×D₃₅₆	—	2	1	no	—
117	C₂×D₃₅₆	—	2	1	no	—
118	C₂×C₂²⋊D₈₉	—	4	1	no	—
119	C₂×C₄×D₈₉	—	4	1	no	—
120	#13083562	—	8	2	no	—
121	#13083559	—	8	2	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	8	1	no	—
125	C₂×#10623494	—	8	1	no	—
126	C₄⋊Dic₈₉	—	2	1	no	—
127	C₄⋊Dic₈₉	—	2	1	no	—
128	C₄⋊Dic₈₉	—	2	1	no	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	C₄⋊Dic₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	#13083553	—	4	1	no	—
133	#13083553	—	4	1	no	—
134	C₂²⋊Dic₈₉	—	4	1	no	—
135	#13083551	—	4	1	no	—
136	#13083551	—	4	1	no	—
137	C₄×Dic₈₉	—	4	1	no	—
138	#41×C₈₉	—	4	2	no	—
139	#41×C₈₉	—	4	2	no	—
140	C₂×Q₈×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	—	2	1	no	—
143	C₂×D₄×C₈₉	—	2	1	no	—
144	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₈₉	—	2	2	no	—
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
149	M₁₆×C₈₉	—	4	4	no	—
150	M₁₆×C₈₉	—	4	2	no	—
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	4	4	no	—
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
161	C₂²⋊C₄×C₈₉	—	2	2	no	—
162	C₂²⋊C₄×C₈₉	—	2	2	no	—
163	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₈₉	#41	1	1	yes	characteristic
166	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂³×C₈₉	—	2	2	no	—
168	C₂³×C₈₉	#121	1	1	yes	characteristic
169	C₂²×D₈₉	—	4	1	no	—
170	Q₈×C₈₉	—	4	2	no	—
171	D₄×C₈₉	—	2	2	no	—
172	D₄×C₈₉	—	2	2	no	—
173	D₄×C₈₉	—	4	2	no	—
174	D₄×C₈₉	—	4	4	no	—
175	D₄×C₈₉	—	4	2	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₈₉	#135	1	2	yes	—
186	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
190	C₂²⋊D₈₉	—	8	2	no	—
191	C₂×Dic₈₉	—	4	1	no	—
192	C₂×Dic₈₉	—	4	1	no	—
193	C₂×Dic₈₉	—	4	1	no	—
194	D₃₅₆	—	4	1	no	—
195	D₃₅₆	—	4	1	no	—
196	D₃₅₆	—	4	1	no	—
197	D₃₅₆	—	4	1	no	—
198	D₃₅₆	—	8	1	no	—
199	C₄×D₈₉	—	8	2	no	—
200	Dic₁₇₈	—	4	1	no	—
201	Dic₁₇₈	—	4	1	no	—
202	Dic₁₇₈	—	4	1	no	—
203	Dic₁₇₈	—	4	1	no	—
204	Dic₁₇₈	—	8	1	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	—	2	1	no	—
208	C₈×C₈₉	—	2	1	no	—
209	C₈×C₈₉	—	4	2	no	—
210	#10623494	—	4	2	no	—
211	#10623494	—	4	2	no	—
212	C₂²×C₈₉	—	2	1	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	4	2	no	—
215	C₂²×C₈₉	—	4	2	no	—
216	C₂²×C₈₉	—	4	2	no	—
217	C₂²×C₈₉	#463	1	2	yes	—
218	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
219	C₂×D₈₉	—	8	1	no	—
220	C₂×D₈₉	—	8	1	no	—
221	C₂×D₈₉	—	8	1	no	—
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	4	2	no	—
226	C₄×C₈₉	#463	1	2	yes	—
227	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
228	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₈₉	#576	1	1	yes	characteristic
230	C₄×C₈₉	#578	1	1	yes	characteristic
231	Dic₈₉	—	8	1	no	—
232	Dic₈₉	—	8	1	no	—
233	Dic₈₉	—	8	1	no	—
234	#19201	—	89	1	no	maximal, Sylow
235	C₂×C₈₉	—	2	2	no	—
236	C₂×C₈₉	—	8	2	no	—
237	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
238	C₂×C₈₉	#3061	1	1	yes	characteristic
239	C₂×C₈₉	#3067	1	1	yes	characteristic
240	D₈₉	—	16	1	no	—
241	#3246	—	89	1	no	—
242	#3245	—	89	1	no	—
243	#3131	—	89	1	no	—
244	#2931	D₈₉	1	1	yes	characteristic, complemented
245	#1699	—	89	2	no	—
246	#1697	—	89	2	no	—
247	#1683	—	89	2	no	—
248	#1681	—	89	2	no	—
249	C₂×#335	—	89	1	no	—
250	#1550	—	89	1	no	—
251	#1547	—	89	1	no	—
252	C₈₉	#19201	1	1	yes	characteristic, complemented, Sylow
253	C₂×#131	—	2	1	no	—
254	#533	—	89	1	no	—
255	#532	—	89	1	no	—
256	#532	C₂×D₈₉	1	1	yes	characteristic
257	#488	—	178	1	no	—
258	#488	—	178	1	no	—
259	#487	—	89	1	no	—
260	#487	—	89	1	no	—
261	#486	—	89	1	no	—
262	#486	—	89	1	no	—
263	#476	—	89	2	no	—
264	#475	—	178	1	no	—
265	#474	—	89	2	no	—
266	#474	—	178	1	no	—
267	#466	—	178	2	no	—
268	#465	—	178	2	no	—
269	#461	—	89	2	no	—
270	#460	—	178	1	no	—
271	#459	—	89	2	no	—
272	#459	—	178	1	no	—
273	#436	—	2	1	no	—
274	#436	C₂×D₈₉	1	2	yes	—
275	C₈×D₄	—	2	1	no	—
276	C₈×D₄	C₂×D₈₉	1	2	yes	—
277	#423	C₂×D₈₉	1	1	yes	characteristic
278	C₂×C₄⋊C₈	—	89	1	no	—
279	C₂×C₄⋊C₈	—	89	1	no	—
280	#416	—	178	1	no	—
281	#416	—	178	1	no	—
282	#408	—	2	1	no	—
283	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
284	#335	—	89	2	no	—
285	#335	—	89	2	no	—
286	#333	—	89	2	no	—
287	#332	—	89	2	no	—
288	#332	—	89	2	no	—
289	#331	—	89	2	no	—
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	178	1	no	—
292	C₂×SD₁₆	—	178	2	no	—
293	C₂×D₈	—	178	2	no	—
294	#131	—	4	4	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	178	1	no	—
299	C₂²×C₈	—	178	1	no	—
300	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
302	C₄⋊Q₈	—	89	1	no	—
303	C₄⋊Q₈	—	89	1	no	—
304	C₄⋊Q₈	—	89	1	no	—
305	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
306	#127	—	89	1	no	—
307	#127	D₃₅₆	1	1	yes	characteristic
308	#125	—	178	1	no	—
309	#124	—	2	1	no	—
310	#124	—	178	1	no	—
311	C₂²⋊Q₈	—	178	1	no	—
312	C₂²⋊Q₈	—	178	1	no	—
313	#121	—	2	1	no	—
314	#121	—	178	1	no	—
315	#121	—	178	1	no	—
316	#121	D₃₅₆	1	2	yes	—
317	C₄×Q₈	—	178	1	no	—
318	C₄×Q₈	—	178	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	178	1	no	—
321	C₄×D₄	—	178	1	no	—
322	C₄×D₄	C₂²×D₈₉	1	2	yes	—
323	#117	—	178	1	no	—
324	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
325	#107	—	178	2	no	—
326	#106	—	178	2	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	89	2	no	—
329	C₄⋊C₈	—	89	2	no	—
330	C₄⋊C₈	—	178	1	no	—
331	C₄⋊C₈	—	178	1	no	—
332	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
333	#103	—	178	1	no	—
334	#103	—	178	1	no	—
335	#103	—	178	1	no	—
336	#103	—	178	1	no	—
337	#103	—	178	2	no	—
338	#102	—	178	2	no	—
339	#102	—	178	2	no	—
340	#102	—	178	1	no	—
341	#102	—	178	1	no	—
342	#102	—	178	1	no	—
343	#102	—	178	1	no	—
344	#102	—	178	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
348	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
349	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
350	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	#41	—	356	2	no	—
354	#41	—	356	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	178	1	no	—
357	C₂×Q₈	—	178	1	no	—
358	C₂×Q₈	—	178	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	356	1	no	—
363	C₂×D₄	—	178	1	no	—
364	C₂×D₄	—	178	1	no	—
365	C₂×D₄	—	178	1	no	—
366	C₂×D₄	C₂×D₃₅₆	1	2	yes	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	356	1	no	—
369	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
371	C₂²×C₄	#13083574	1	1	yes	characteristic
372	SD₁₆	—	712	2	no	—
373	D₈	—	712	2	no	—
374	M₁₆	—	4	4	no	—
375	M₁₆	—	4	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	—	178	2	no	—
381	C₂×C₈	—	178	2	no	—
382	C₂×C₈	—	712	1	no	—
383	C₂×C₈	—	712	1	no	—
384	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	356	1	no	—
390	C₄⋊C₄	—	356	1	no	—
391	C₄⋊C₄	—	178	1	no	—
392	C₄⋊C₄	—	178	1	no	—
393	C₄⋊C₄	—	178	1	no	—
394	C₄⋊C₄	—	178	1	no	—
395	C₄⋊C₄	—	178	1	no	—
396	C₄⋊C₄	—	178	1	no	—
397	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	356	1	no	—
401	C₂²⋊C₄	—	356	1	no	—
402	C₂²⋊C₄	—	356	1	no	—
403	C₄²	—	356	1	no	—
404	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
405	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
406	C₄²	#13083574	1	1	yes	characteristic
407	C₄²	C₂³×D₈₉	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	—	356	1	no	—
410	C₂³	#15667986	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	356	1	no	—
413	Q₈	—	356	1	no	—
414	Q₈	—	356	1	no	—
415	Q₈	—	356	1	no	—
416	Q₈	—	712	1	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	356	1	no	—
423	D₄	—	356	1	no	—
424	D₄	—	356	1	no	—
425	D₄	—	356	1	no	—
426	D₄	—	712	1	no	—
427	D₄	—	712	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	356	1	no	—
435	C₂×C₄	—	356	1	no	—
436	C₂×C₄	—	356	1	no	—
437	C₂×C₄	—	712	2	no	—
438	C₂×C₄	#15667986	1	1	yes	characteristic
439	C₂×C₄	#15667986	1	1	yes	characteristic
440	C₂×C₄	#15667986	1	1	yes	characteristic
441	C₂×C₄	#15668032	1	2	yes	—
442	C₂×C₄	#15668038	1	2	yes	—
443	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
445	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	356	2	no	—
452	C₈	—	356	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	712	1	no	—
459	C₂²	—	712	1	no	—
460	C₂²	—	712	1	no	—
461	C₂²	#19151813	1	2	yes	—
462	C₂²	C₂×#15667986	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	712	1	no	—
468	C₄	—	712	1	no	—
469	C₄	—	712	1	no	—
470	C₄	#19151813	1	2	yes	—
471	C₄	C₂×#15668032	1	1	yes	characteristic
472	C₄	C₂×#15668038	1	1	yes	characteristic
473	C₄	#19152403	1	1	yes	characteristic
474	C₄	#19152415	1	1	yes	characteristic
475	C₂	—	2	2	no	—
476	C₂	—	8	2	no	—
477	C₂	—	1424	1	no	—
478	C₂	C₂×#19151813	1	1	yes	characteristic
479	C₂	#26029922	1	1	yes	characteristic
480	C₂	#26029972	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2931	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26031559	C₂
hypercenter	#2931	D₈₉
hypocenter	C₈₉	#19201
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2931

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #26031568	C₂	semidirect
3. #26030575	C₂	semidirect
4. #26019799	C₂	semidirect
5. #26019785	C₂	semidirect
6. #26019703	C₂	semidirect
7. #26019689	C₂	semidirect
8. C₂×#19151351	C₂	semidirect
9. #26018943	C₂	semidirect
10. #26018930	C₂	semidirect
11. C₈₉×#2931	C₂	semidirect
244. #2931	D₈₉	semidirect
252. C₈₉	#19201	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#26031568	2
#26031559	2
#26030575	2
#26019799	2
#26019785	2
#26019703	2
#26019689	2
C₂×#19151351	2
#26018943	2
#26018930	2
C₈₉×#2931	2
#19201	89